23.5.90 problem 90

Internal problem ID [6699]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 5. THE EQUATION IS LINEAR AND OF ORDER GREATER THAN TWO, page 410
Problem number : 90
Date solved : Tuesday, September 30, 2025 at 03:50:56 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime }+\left (2+x \right ) y^{\prime \prime }+\left (2+x \right )^{2} y^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 26

ode:=diff(y(x),x)+(x+2)*diff(diff(y(x),x),x)+(x+2)^2*diff(diff(diff(y(x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 +c_2 \left (2+x \right ) \sin \left (\ln \left (2+x \right )\right )+c_3 \left (2+x \right ) \cos \left (\ln \left (2+x \right )\right ) \]

✓ Mathematica. Time used: 0.069 (sec). Leaf size: 40

ode=D[y[x],x] + (2 + x)*D[y[x],{x,2}] + (2 + x)^2*D[y[x],{x,3}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} (x+2) ((c_1-c_2) \cos (\log (x+2))+(c_1+c_2) \sin (\log (x+2)))+c_3 \end{align*}

✓ Sympy. Time used: 0.208 (sec). Leaf size: 7

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x + 2)**2*Derivative(y(x), (x, 3)) + (x + 2)*Derivative(y(x), (x, 2)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x \]